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nalin [4]
3 years ago
7

Tanya and Kim are going to see a movie. The clocks show when the movie begins and ends. How long will the movie last? A.2 hours,

45 minutes B.1 hour, 15 minutes C.2 hours D.1 hour, 45 minutes PS: The time is 4 : 15
Mathematics
1 answer:
Tems11 [23]3 years ago
3 0
Where are the clocks?

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A spring has natural length 0.75 m and a 5 kg mass. A force of 8 N is needed to keep the spring stretched to a length of 0.85 m.
I am Lyosha [343]
Use Hooke's law to find the spring constant. If it takes 8N to stretch the spring by 0.1m, then

8\text{ N}=k(0.1\text{ m})\implies k=80\dfrac{\text N}{\text m}

I'm going to assume the spring is fixed to a ceiling, and that any stretching in the downward direction counts as movement in the positive direction. The spring's motion is then modeled by

y''(t)+80y(t)=0

where y(t) is the position of the spring's free end as it moves up and down. Solving this is easy enough: the characteristic solution will be

y(t)=C_1\cos4\sqrt5t+C_2\sin4\sqrt5t

Given that the spring is stretched to a length of 1m (a difference of 0.25m from its natural length), and is released with no external pushing or pulling, we have the two initial conditions y(0)=\dfrac14 and y'(0)=0.

y(0)=\dfrac14\implies\dfrac14=C_1\cos0+C_2\sin0\implies C_1=\dfrac14
y'(0)=0\implies 0=-4\sqrt5C_1\sin0+4\sqrt5C_2\cos0\implies C_2=0

So the spring's motion is dictated by the function

y(t)=\dfrac14\cos4\sqrt5t
8 0
3 years ago
Name the factors of 8m^2
Leto [7]

Answer: Factor 8m^2+30m+7. 8m2+30m+7 8 m 2 + 30 m + 7.

Step-by-step explanation:

5 0
2 years ago
10 increased by twice Chrissy's height Use the variable c to represent Chrissy's height.
ahrayia [7]

Answer:

2C + 10

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
-2 times g(4) when g(x) =-x squared+(4x)-11
andrezito [222]

Answer:

+22

Step-by-step explanation:

Given g(x) = -x^2 + 4x - 11, g(4) is -(4)^2 + 4(4) - 11, or just -11.

Then -2 times g(4) = -2(-11) = +22

3 0
3 years ago
If f(-7)=7 what is the corresponding order pair solution?
choli [55]

its absoulte value

so the answer is 7

3 0
3 years ago
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